Triple

T18480260
Position Surface form Disambiguated ID Type / Status
Subject Orthogonal Polynomials E451537 entity
Predicate contains P35 FINISHED
Object Christoffel–Darboux formula — NE NERFINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Christoffel–Darboux formula | Statement: [Orthogonal Polynomials, contains, Christoffel–Darboux formula]

Disambiguation candidates (1 decision)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Christoffel–Darboux formula
Context triple: [Orthogonal Polynomials, contains, Christoffel–Darboux formula]
  • A. Christoffel–Darboux formula chosen
    The Christoffel–Darboux formula is a key result in the theory of orthogonal polynomials that provides an explicit expression for sums of products of such polynomials, with important applications in approximation theory and mathematical physics.
  • B. Rodrigues formula
    Rodrigues formula is a classical representation that expresses certain families of orthogonal polynomials, such as Jacobi polynomials, in terms of derivatives of weight functions.
  • C. Christoffel–Schwarz formula
    The Christoffel–Schwarz formula is a fundamental result in complex analysis that provides an explicit conformal mapping from the upper half-plane onto polygonal regions in the complex plane.
  • D. Gegenbauer polynomials
    Gegenbauer polynomials are a family of orthogonal polynomials on the interval [-1, 1] that generalize Legendre polynomials and play a key role in harmonic analysis and solutions of differential equations with spherical symmetry.
  • E. Jack polynomials
    Jack polynomials are a family of symmetric polynomials depending on a continuous parameter that generalize several classical symmetric functions and play a key role in algebraic combinatorics, representation theory, and mathematical physics.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 batches)

Stage Batch ID Job type Status
creating batch_69d8d38465a0819099b9b42d2a662ac1 elicitation completed
NER batch_69e53066a7108190a50eda9b489c90ca ner completed
Created at: April 10, 2026, 11:35 a.m.